In: Statistics and Probability
The table to the below contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below.
X1 |
X2 |
X3 |
|
Y1 |
34 |
40 |
55 |
36.86 |
43.24 |
48.91 |
|
Y2 |
18 |
21 |
14 |
15.14 |
17.76 |
20.09 |
(a) Compute the value of the chi-square test statistic. (Round to three decimal places as needed.)
X 2/0=
(b) Test the hypothesis that X and Y are independent at the alpha equals 0.01 level of significance.
H0: mu x = Ex and mu y = Ey; H1: mu x does not = Ex or mu y does not = Ey
H0: Y category and X category are independent; H1: The Y category and X category are dependent.
H0: Y category and X category are dependent; H1: The Y category and X category are independent.
H0: Y category and X category have equal proportions; H1: The proportions are not equal.
(c) What range of P-values does the test statistic correspond to? The P-value is ?
(d) Should the null hypothesis be rejected?